A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?
The bob of the simple pendulum will experience the acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car. Acceleration due to gravity =g Centripetal acceleration =v2/R where, v is the uniform speed of the car R is the radius of the track Effective acceleration (g′) is given as: g′=g2+R2v4 ∴ Time peroid, t=2πg′l =2πg2+R2v4l
